If the nucleus of an atom is enlarged to the size of a ball of 10 cm diameter, the atom would look like a sphere of diameter roughly equal to

Options

A. 10m
B. 10km
C. 100km
D. 1000km

Answer

To solve the problem, we need to determine the size of an atom when the nucleus is enlarged to a diameter of 10 cm. We will follow these steps:

### Step-by-Step Solution:

1. **Understand the Sizes of Nucleus and Atom**:
- The typical size of a nucleus is approximately \(10^{-15}\) meters.
- The typical size of an atom is approximately \(10^{-10}\) meters.

2. **Calculate the Ratio of Sizes**:
- The ratio of the size of the atom to the size of the nucleus can be calculated as follows:
\[ \text{Ratio} = \frac{\text{Size of Atom}}{\text{Size of Nucleus}} = \frac{10^{-10} \text{ m}}{10^{-15} \text{ m}} = 10^{5} \]
This means that the atom is about \(10^5\) times larger than the nucleus.

3. **Enlarge the Nucleus to 10 cm**:
- If the nucleus is enlarged to a diameter of 10 cm, we need to express this in meters:
\[ 10 \text{ cm} = 0.1 \text{ m} \]

4. **Calculate the Size of the Atom**:
- Since the nucleus is now 0.1 m, we can find the size of the atom using the ratio we calculated:
\[ \text{Size of Atom} = \text{Size of Nucleus} \times \text{Ratio} = 0.1 \text{ m} \times 10^{5} \]
\[ = 10^{4} \text{ m} \]

5. **Convert Meters to Kilometers**:
- To convert meters to kilometers, we divide by 1000:
\[ 10^{4} \text{ m} = 10^{4} \div 1000 = 10 \text{ km} \]

### Final Answer:
The diameter of the atom would be roughly equal to **10 kilometers**.